There are lots of graphs you could use. Not all are great choices. Many times choosing simple and familiar graph types is the best choice. We have bar, column, line, histograms (and Pareto), area, pie, donut, scatter, box and whisker, heat maps and others.
For data visualization, some people say that there are seven primary types of charts: column, line, pie, horizontal bar, area, scatter, and combo. The horizontal bar is really just a column chart with the columns horizontal. Included in the definition of the column chart, (and bar chart) is the stacked chart and the clustered column. Stephen Few, author of the book Show Me the Numbers mentions that he doesn’t really use pie charts. Neither does Cole Nussbaumer Knaflic author of the book Storytelling with Data. Both authors would rather choose a different chart type.
Tableau has a paper called Which chart or graph is right for you?. Which chart types do they suggest? Bar, Line, Pie, Map, Scatter, Gantt, Bubble, Histogram, Bullet, Heat, Highlight table, Treemap, and Box and whisker.
The most important ones, in my opinion, are bar, column, line, scatter, box and whisker, map and combo chart. Some of the other charts are better off being swapped out for other ones. For example, the pie chart is often better communicated to the user with a bar or column chart, unless the number of segments is 3 or less. The area chart could be replaced with two line charts: one for the total and the other one for the parts. The radar chart is another one that could possibly be replaced with a bar graph or line graph.
Column (or Bar)
A column chart (vertical bars) is a good choice for displaying many types of data, perhaps the most versatile chart of all. It is good for showing numbers and categories. For example, comparing sales of product categories. You would have currency units on the y-axis and categories on the x-axis. Your y-axis might have different sales channels such as Web and Direct. You could chart the population by city, or expenses by department, or the number of employees by department.
Histogram
A histogram is shown with a column or bar chart, but it is very different than the previous examples. Histograms show frequencies. On the x-axis you have bins or ranges of values. On the y-axis, you have frequency values. It measures how often something occurs. For example you might have a list of students and their heights in inches. You could create bins that represent ranges of heights, in order. Another example is the number of days it takes for the packages to be shipped out of the warehouse from the time the order was placed.
Line
Line charts are commonly used to visualize quantities over time. Time is on the y-axis. You could show stock price by the hour. You could show profit by month. You could combine charts into an Excel combo chart that uses a line chart and a column chart to show and compare two different types of quantities. You can use linear or polynomial trendlines to visualize data or forecast future data.
Scatter
The scatter plot is also a very popular and versatile chart.
Charts and Color
Stephen Few, in his book Show Me the Numbers in chapter 12 lists several charts that he feels should be replaced with a different type of chart. Chapter 12 is called Silly Charts That Are Best Foresaken. Here is his list of avoidable charts: donut charts, radar chats, area charts for combining part-to-whole and time-series relationships, circle charts (circle inside another circle), unit charts, funnel charts, and waterfall charts for simple part-to-whole relationships. In general, avoid using these types of charts. Try to find a different chart. If you are looking for a color palette, Mr. Few has a light, medium and dark palette over at github. Over at github there is a link to an article called Practical Rules for Using Color in Charts under the References section.